Geometry370 views·Updated Jun 14, 2026·2 pages

Understanding the Pythagorean Theorem for Right Triangles

LUCY@lucylooloo

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The Pythagorean Theorem is one of the most useful math...

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# The Pythagorean Theorem

A triangle that contains a right angle (an angle that measures 90°, symbolized by a small square "") is
called a

Understanding the Pythagorean Theorem

Right triangles have one 90° angle (marked with a small square) and three sides: two shorter sides called legs (labeled "a" and "b") and one longer side called the hypotenuse (labeled "c"). The hypotenuse is always opposite to the right angle.

The Pythagorean Theorem states that $a^2 + b^2 = c^2$ . In other words, if you square the lengths of both legs and add them together, you'll get the square of the hypotenuse. This powerful relationship works for every right triangle, no matter its size!

When you know two sides of a right triangle, finding the third is easy. For example, if leg a = 3 feet and leg b = 4 feet, you can find the hypotenuse by plugging these values into the formula: $c^2 = 3^2 + 4^2 = 9 + 16 = 25$ . Since $c^2 = 25$ , taking the square root gives us c = 5 feet.

Math Magic! The 3-4-5 triangle is a special right triangle where the sides form a perfect Pythagorean triple. Whenever you see these numbers as the sides of a triangle, you know it's a right triangle!

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Real-World Applications

The Pythagorean Theorem helps solve many everyday problems involving right angles. Let's see how it works in real situations!

In a sail-making example, imagine cutting sailcloth diagonally where the width is 5 meters and the diagonal cut is 13 meters. To find the length, set up the equation: $a^2 + 5^2 = 13^2$ , which becomes $a^2 + 25 = 169$ . Solving for $a^2$ gives us $a^2 = 144$ , so $a = 12$ meters. The sailcloth is 12 meters long.

Another example: two cars leave from the same spot, one traveling 8 miles north and the other 6 miles east. How far apart are they? The distance between them forms the hypotenuse of a right triangle. Using the theorem: $d^2 = 6^2 + 8^2 = 36 + 64 = 100$ . Taking the square root gives us $d = 10$ miles.

Try This! Next time you're in a rectangular room, try measuring the diagonal distance from one corner to the opposite corner using the Pythagorean Theorem instead of a tape measure!

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Geometry370 views·Updated Jun 14, 2026·2 pages

Understanding the Pythagorean Theorem for Right Triangles

LUCY@lucylooloo

Add to Google sources

The Pythagorean Theorem is one of the most useful math tools you'll ever learn! It shows the relationship between the sides of a right triangle and helps solve countless real-world problems. This simple formula opens the door to finding unknown...

of 2

Understanding the Pythagorean Theorem

Math Magic! The 3-4-5 triangle is a special right triangle where the sides form a perfect Pythagorean triple. Whenever you see these numbers as the sides of a triangle, you know it's a right triangle!

of 2

Real-World Applications

The Pythagorean Theorem helps solve many everyday problems involving right angles. Let's see how it works in real situations!

Try This! Next time you're in a rectangular room, try measuring the diagonal distance from one corner to the opposite corner using the Pythagorean Theorem instead of a tape measure!